Cantilever with uniformly distributed load – shape of the shear force diagram For a cantilever beam carrying a uniformly distributed load over its entire length, the shear force diagram has the shape of a:

Introduction / Context:
Drawing shear force (V) and bending moment (M) diagrams quickly from load diagrams is a core skill in structural analysis. Recognizing the characteristic shapes helps double-check calculations and speed up problem solving.

Given Data / Assumptions:

• Cantilever beam of length L, fixed at one end and free at the other.
• Uniformly distributed load w (force per unit length) over the full span.
• Static equilibrium, small deflections.

Concept / Approach:
For a UDL, the shear force is the integral of load intensity with negative sign conventionally: dV/dx = −w. Hence V varies linearly with x. At the free end of a cantilever V = 0, and at the fixed end V = wL (magnitude). Therefore, the shear diagram is triangular.

Step-by-Step Solution:
Start from the free end: V(0) = 0.Integrate load: V(x) = −w x (sign per convention); magnitude grows linearly with x.At the fixed end x = L: |V(L)| = w L, confirming a straight line from 0 to wL.

Verification / Alternative check:
Differentiate the bending moment diagram M(x) = −w x^2 / 2; dM/dx = V(x) gives the same linear variation.

Why Other Options Are Wrong:

• Rectangle implies constant shear, which corresponds to a point load, not a UDL.
• Parabola or cubic parabola describe M(x) shapes, not V(x) for a UDL on cantilever.
• Straight line with zero slope would be constant shear, again incorrect.

Common Pitfalls:
Mixing up signs or confusing shapes of V and M; remember: UDL ⇒ V linear, M quadratic.

Final Answer:
Triangle